GoodNodes(e|H, mu)
GoodNodes(e|H, mu, r)
Given a partition and an integer e, Kleshchev [K] defined the notion
of good node for each residue r (0 le r
By definition, there is at most one good node for each residue r,
and this node is a removable node (in the diagram of mu). The
function
The good nodes also determine the Kleshchev--Mullineux map (see
D
(mu) in the symmetric
group case. Brundan~[B] has recently generalized this result to the
Hecke algebra.
GoodNodes
returns a list of the rows of mu which end
in a good node; the good node of residue r (if it exists) is the
(r+1)--st element in this list. In the second form, the number of
the row which ends with the good node of residue r is returned; or
false
if there is no good node of residue r.
gap> GoodNodes(5,[5,4,3,2]);
[ false, false, 2, false, 1 ]
gap> GoodNodes(5,[5,4,3,2],0);
false
gap> GoodNodes(5,[5,4,3,2],4);
1
GoodNodeSequence
GoodNodeSequence and Mullineux
Mullineux). This function requires the package ``specht'' (see
RequirePackage).
April 1997